I checked
Aurcade.com for Florida locations and then Google mapped them to find the ones closest to Delray Beach. There were a dozen or so within 50 miles but they all have new games almost exclusively, no classics to speak of.
You're gonna be about 35 miles from Hollywood, Florida, though, so you can pay a visit to
Billy Mitchell's restaurant. I'm told the food there is very good, as is his hot sauce. Aurcade says they have a
Ms. Pac-Man and a
Daytona USA, but the entry hasn't been updated since 2008, so who knows what, if anything, they have now.
Also,
Apollo Amusements is in Fort Lauderdale, about 28 miles away. Apollo Amusements is a retail game room vendor. They had a location in Pompano Beach some years back that was the site for a
Guinness event in April 2006, where some of the top classic arcade gamers converged to set some records, a little footage of which can be seen in The King of Kong.